Overcoming confounds and improving the
interpretability of connectivity analyses
Eugene Duff
!
GlaxoSmithKline - Neurophysics Workshop on Skeptical Neuroimaging
Brain connectivity in neuroimaging
Sporns, 2007
Friston, 1995
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Connectivity from uncontrolled
fluctuations
Biswal 1995
Smith 2009
Brain Connectivity from uncontrolled fluctuations
Functional connectivity analyses
Distinct patterns of brain activity in young carriers
of the APOE-!4 allele
Nicola Filippinia,b,c, Bradley J. MacIntoshb, Morgan G. Houghb, Guy M. Goodwina, Giovanni B. Frisonic,
Stephen M. Smithb, Paul M. Matthewsd,e, Christian F. Beckmannb,e, and Clare E. Mackaya,b,1
aUniversity Department of Psychiatry and bFunctional Magnetic Resonance Imaging of the Brain Centre, University of Oxford, Oxford OX3 9DU, United
Kingdom; cLaboratory of Epidemiology, Neuroimaging, and Telemedicine, Istituto di Ricovero e Cura a Carattere Scientifico San Giovanni di
Dio-Fatebenefratelli, Brescia 25125, Italy; dGlaxoSmithKline Research and Development, Clinical Imaging Centre, London W12 0NN, United Kingdom;
and eDepartment of Clinical Neuroscience, Imperial College, Hammersmith Campus London W12 0NN, United Kingdom
hippocampus ! memory ! neuroimaging ! resting connectivity
A
Johnstone JM 2008
Seed region
polipoprotein E (apoE, protein; APOE, gene) is a very-lowdensity lipoprotein that removes cholesterol from the blood
and carries it to the liver for processing (1). In the central nervous
system, apoE has a key role in coordinating the mobilization and
redistribution of cholesterol, phospholipids, and fatty acids, and it
is implicated in mechanisms such as neuronal development, brain
plasticity, and repair functions (2). The human APOE gene, which
is encoded on chromosome 19, has 3 allelic variants (!2, !3, and !4).
The !4 allele has been associated with a higher risk of cardiovascular disease (3), both early-onset (4) and late-onset (5) Alzheimer’s disease (AD), poor outcome from traumatic brain injury (6),
and age-related cognitive impairment (7).
Neuroimaging studies of the APOE polymorphism in healthy
subjects have largely focused on gray matter (GM) alterations in
middle or late life, particularly in brain regions associated with
the greatest AD pathological findings. Even in asymptomatic
subjects, hippocampal and frontotemporal GM reduction has
been observed in APOE !4-carriers relative to noncarriers (8).
Moreover, a reduction of resting glucose metabolism was reported in young and middle-aged cognitively normal APOE
!4-carriers in brain regions known to be affected by AD,
including the posterior cingulate, parietal, temporal, and prefrontal cortices (9–11). fMRI task-based studies (mainly investigating memory processes) have shown greater activation in
middle-aged and elderly APOE !4-carriers relative to noncarriers (12–16). Although these studies suggest an influence of the
APOE !4 allele on brain structure and metabolism, they do not
make clear at what age these influences initially manifest.
Furthermore, although differences in structure, resting metabolism, and function have each been reported in !4-carriers
relative to noncarriers, it remains to be established to what extent
these characteristics interact.
Thus far, reports of structural and functional effects of the
APOE !4 allele in young adults are limited (17–20). Only 2 small
fMRI studies have tested for early life associations of the APOE
polymorphism with changes in brain function. Filbey et al. (18)
reported greater activation in 8 APOE !4-carriers compared with
8 noncarriers in medial frontal and anterior cingulate areas using
a working memory paradigm. Mondadori et al. (17) reported
reduced activation with an associative learning paradigm in 13
!4-carriers relative to 11 !2-carriers and 10 !3-homozygotes.
Both studies therefore suggest that the APOE genotype influences brain functions even early in adulthood.
Here, we used a multimodal MRI protocol to investigate
structural and functional neurophysiological characteristics of 18
APOE !4-carriers and 18 noncarriers, with ages ranging from 20
to 35 years old. Our first aim was to measure differences in
spontaneous fluctuations in resting brain function in !4-carriers
relative to noncarriers using resting-state fMRI. Brain regions
showing a strong temporal coherence (coactivation) in lowfrequency fluctuations (less than 0.1 Hz) are defined as ‘‘resting
state networks’’ (RSNs), and they reflect intrinsic properties of
functional brain organization (21). We were specifically interested in studying the effect of the APOE !4 allele on an RSN
called the ‘‘default mode network’’ (DMN), which includes the
prefrontal, anterior and posterior cingulate, lateral parietal, and
inferior/middle temporal gyri; cerebellar areas; and thalamic
nuclei and extending to mesial temporal lobe (MTL) regions
(22). The DMN is affected by neurodegenerative processes (23);
both AD patients (24) and people with amnestic mild cognitive
impairment (aMCI) (25) are reported to have reduced coactivation of hippocampal and posterior cingulate regions.
Our second aim was to test for the effects of APOE genotype
on task-related activations. Because the MTL and hippocampi,
in particular, are the earliest brain regions to show pathological
signs in AD (26), and because APOE receptors in the brain are
mainly expressed in the hippocampal-entorhinal cortex complex
(27), we selected a blood oxygen level-dependent (BOLD) fMRI
task that preferentially activates MTL regions: the ‘‘novel vs.
familiar’’ memory-encoding paradigm has been widely used to
demonstrate robust hippocampal activation (28, 29).
Finally, we tested whether resting or task-related BOLD
differences between !4-carriers and noncarriers were associated
with underlying subject-specific anatomical or resting brain
perfusion (30) measures.
NEUROSCIENCE
Edited by Robert W. Mahley, The J. David Gladstone Institutes, San Francisco, CA, and approved March 6, 2009 (received for review November 25, 2008)
The APOE !4 allele is a risk factor for late-life pathological changes
that is also associated with anatomical and functional brain
changes in middle-aged and elderly healthy subjects. We investigated structural and functional effects of the APOE polymorphism
in 18 young healthy APOE !4-carriers and 18 matched noncarriers
(age range: 20 –35 years). Brain activity was studied both at rest
and during an encoding memory paradigm using blood oxygen
level-dependent fMRI. Resting fMRI revealed increased ‘‘default
mode network’’ (involving retrosplenial, medial temporal, and
medial-prefrontal cortical areas) coactivation in !4-carriers relative
to noncarriers. The encoding task produced greater hippocampal
activation in !4-carriers relative to noncarriers. Neither result could
be explained by differences in memory performance, brain morphology, or resting cerebral blood flow. The APOE !4 allele
modulates brain function decades before any clinical or neurophysiological expression of neurodegenerative processes.
Dual Regression
www.pnas.org"cgi"doi"10.1073"pnas.0811879106
Results
Participants. APOE !4-carriers and noncarriers were matched for
age, gender, and years of education, and 2 individuals in each
group had a family history of dementia (either first or second
Author contributions: N.F., B.J.M., P.M.M., and C.E.M. designed research; N.F. and C.E.M.
performed research; N.F., B.J.M., M.G.H., S.M.S., C.F.B., and C.E.M. analyzed data; and N.F.,
G.M.G., G.B.F., P.M.M., and C.E.M. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1To
whom correspondence should be addressed. E-mail: clare.mackay@psych.ox.ac.uk.
PNAS Early Edition ! 1 of 6
Psycho-physiological interactions
Analysis of graph theoretic measures
Reasons for skepticism..
With no model of signal, analyses will be extremely sensitive to variations in noise:
X
𝜌xa,ya
Y
Healthy
Differences in patient
groups (e.g. vascular tone)
Patients
X
𝜌xa,ya
Differences across activation states
(e.g. BOLD ceiling)
Y
condition 1
condition 2
.
Reasons for skepticism..
Correlation on its own in general provides little insight the changes/differences in signal
X
𝜌xa,ya
Y
Region 1
Region 2
X
Y
x
y
Increase in noise
𝜌xa,ya
Increase in signal levels
𝜌xa,ya
𝜌xa,ya
Increase in common activity in one of two regions
𝜌xa,ya
Increase in unrelated activity in one of two regions
𝜌xa,ya
Synchronisation of signals across regions (coupling)
Dynamic Causal Modelling
.
DCM of random fluctuations
Stochastic DCM: models endogenous stochastic fluctuations!
! !
- Variational Bayesian generalised filtering estimation! !
!
! !
- Communicated dynamics are modelled to have low frequency dynamics!
Recent alternate approach uses deterministic
model using on cross-spectra of time series.!
Strengths:!
Models can distinguish SNR changes, different
types of inter-regional connectivity topologies!
Generative model: !
- estimates physiological variables (pharma)!
! - can be used to generate expected observable
statistics such as correlation, graph-theoretic
measures, etc.!
Friston et al, Math Prob Eng 2010;Friston et al Neuroimage 2011; Friston et al Neuroimage 2014
DCM of random fluctuations
Stochastic DCM: models endogenous stochastic fluctuations!
! !
- Variational Bayesian generalised filtering estimation! !
!
! !
- Communicated dynamics are modelled to have low frequency dynamics!
Recent alternate approach uses deterministic
model using on cross-spectra of time series.!
Limitations:!
Models are complex, computationally challenging:!
! - require ROI definition - not mapping!
! - test limited numbers of model topologies !
! - may not account for/identify large-scale
dynamics!
! - high-dimensional models - may difficult to
interpret !
!
Friston et al, Math Prob Eng 2010;Friston et al Neuroimage 2011; Friston et al Neuroimage 2014
Goal
!
Identify a simple approach to characterising connectivity that can provide
some of the insight provided by DCM, while still enabling mapping.!
!
Strategy:!
Focus on identification of types of pairwise changes in relationship!
!
!
.
Basic features of dynamics affecting connectivity
X
𝜌xa,ya
Y
Region 1
Region 2
X
Y
x
y
Increase in noise
BOLD signal
𝜌xa,ya
Increase in signal levels
Change in SNR
𝜌xa,ya
Increase in common activity in one of two regions
𝜌xa,ya
Increase in unrelated activity in one of two regions
𝜌xa,ya
Synchronisation of signals across regions
𝜌xa,ya
Basic features of dynamics affecting connectivity
X
𝜌xa,ya
Y
σxa
Region 1
Region 2
X
Y
x
y
σya
Increase in noise
𝜌xa,ya
σxa
σya
Increase in signal levels
Change in SNR
𝜌xa,ya
σxa
σya
Increase in common activity in one of two regions
𝜌xa,ya
σxa
σya
Increase in unrelated activity in one of two regions
𝜌xa,ya
σxa
σya
Synchronisation of signals across regions
BOLD signal
𝜌xa,ya
σxa
σya
Shared/Unshared Signal Model
Pairwise model linking regions X and Y.
Condition a
S
Model Formulation
BOLD signal for condition a as a function of S and Ux Uy.
Shared signal
(1)
w2 ya
w2 xa
proportion of shared signal y
(2)
Proportion of shared signal in each region is bounded by correlation
Y
X
Ux
(3)
Uy
(4)
Unshared signal (y)
Unshared signal (x)
(5)
BOLD signal
y
x
𝜌xa,ya
BOLD statistics (corr,var)
σxa
Condition b produces some change in levels of shared and unshared signals
- wxb = cx wxa, wyb = cy wya. , matching the total change in variance:
σya
(6)
Condition b
S
Shared signal
New observed variance can be expressed:
w2yb
w2xb
(7)
proportion of shared signal (y)
𝜌xb,yb can be expressed in terms of σxa,σxb σya, σyb, way, and ux
Ux
Y
X
Uy
Unshared signal (y)
Unshared signal (x)
(8)
(9)
(10)
BOLD signal
y
x
𝜌xb,yb
BOLD statistics (corr,var)
σxb
σyb
Given the limits on way, maximum effects of particular changes in signal and
noise on 𝜌xb,yb can be determined based on variance changes. E.g. if there
was no change in signal levels:
Determining possibility of different changes
𝜌xa,ya σxa,σxb σya, σyb,
𝜌xb,yb
X
𝜌x,y
Y
σxa
cx=1 (ux>1)
σya
cy=1 (uy>1)
σxa
cx>1 (ux=1)
σya
cy>1 (uy=1)
σxa
cx>1 (ux=1)
σya
cy=1 (uy=1)
σxa
cx=1 (ux>1)
σya
cy=1 (uy=1)
σxa
cx>1 (ux<1)
σya
cy>1 (uy<1)
Increase in noise
𝜌x,y
Increase in signal levels
Change in SNR
𝜌x,y
Increase in common activity in one of two regions
𝜌x,y
Increase in unrelated activity in one of two regions
𝜌x,y
Synchronisation of signals across regions (coupling)
Determining possibility of different changes
𝜌xb,yb σxa,σxb σya, σyb,
𝜌xa,ya
X
𝜌x,y
Y
σxa
cx=1 (ux>1)
σya
cy=1 (uy>1)
σxa
cx>1 (ux=1)
σya
cy>1 (uy=1)
σxa
cx>1 (ux=1)
σya
cy=1 (uy=1)
σxa
cx=1 (ux>1)
σya
cy=1 (uy=1)
σxa
cx>1 (ux<1)
σya
cy>1 (uy<1)
Increase in noise
𝜌x,y
Increase in signal levels
Change in SNR
𝜌x,y
Increase in common activity in one of two regions
𝜌x,y
Increase in unrelated activity in one of two regions
𝜌x,y
Synchronisation of signals across regions (coupling)
Experiment
!
Are changes in connectivity across associated with variance changes?!
Do these changes correspond to particular types of changes in connectivity
- are they predicted by model?!
How about activation levels?!
Results
Proportion
Variance changes from rest for visual
Variance changes from rest for motor
Proportion of edges with at least
one region changing in variance
Number of edges
Change in correlation (z-score)
Results
Variance changes from rest for visual
No change in variance.
Rest
!
Visual movie
Variance changes from rest for motor
One region increases in variance
Both regions increase in variance
Results
Variance changes from rest for visual
Variance changes from rest for motor
Correlation
Correlation with V1
Correlation with Precuneus
Correlation with M1
Results
Variance changes from rest for visual
Variance changes from rest for motor
Significant reductions in in correlation
Correlation
Correlation with V1
Correlation with Precuneus
Changes indicative of decoupling
Visual task - Rest (V1 seed)
Correlation changes from rest for visual
Correlation with M1
Results
Variance changes from rest for visual
Variance changes from rest for motor
Significant reductions in in correlation
Correlation
Correlation with V1
Correlation with Precuneus
Changes indicative of decoupling
Visual task - Rest (V1 seed)
Correlation changes from rest for visual
Increase in signal levels
Correlation with M1
Results
Variance changes from rest for visual
Variance changes from rest for motor
Significant reductions in in correlation
Correlation
Correlation with V1
Correlation with Precuneus
Changes indicative of decoupling
Visual task - Rest (V1 seed)
Correlation changes from rest for visual
Increase in unshared signal
Correlation with M1
Results
Variance changes from rest for visual
Variance changes from rest for motor
Significant reductions in in correlation
Correlation
Correlation with V1
Correlation with Precuneus
Changes indicative of decoupling
Visual task - Rest (V1 seed)
Correlation changes from rest for visual
Reduction in shared signal
Correlation with M1
Results
Variance changes from rest for visual
Variance changes from rest for motor
Significant reductions in in correlation
Correlation
Correlation with V1
Correlation with Precuneus
Changes indicative of decoupling
Visual task - Rest (V1 seed)
Correlation changes from rest for visual
Decoupling
Correlation with M1
Summary
We have identified a simple model that links correlation and variance to provides insight into
the types of dynamics underlying connectivity changes!
In a test dataset we could find almost every proposed feature of dynamics!
Most changes in correlation are accompanied by some change in variance!
DCM models typically predict variance changes, so are validated by these results!
Software is under development!
!
Future
directions
!
Smooth integration with functional connectivity and DCM analyses!
More signal components: relationship to ICA?!
!
!
.
Acknowledgements
!
Steve Smith!
Sasi Madugula!
Mark Woolrich!
Tamar Makin!
!
!
!
!
.